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Here we follow Dyson's philosophy (Ref. 30). In fact, he also found ten symmetry classes, though a coarser division into only three classes appears in the final answer. This is because Dyson considers the action of symmetries on the Hilbert space of a many-body system. Unlike the Nambu space, the Hilbert space of quantum states has no canonical conjugation, since the multiplication by a phase is an intrinsic symmetry.
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Here we follow Dyson's philosophy (Ref. 30). In fact, he also found ten symmetry classes, though a coarser division into only three classes appears in the final answer. This is because Dyson considers the action of symmetries on the Hilbert space of a many-body system. Unlike the Nambu space, the Hilbert space of quantum states has no canonical conjugation, since the multiplication by a phase is an intrinsic symmetry.
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-, or by changing k to 2 - k. We have chosen not to do that because the variable change k 2 - k is convenient in the free-fermion context; see Ref. 2. © 2011 American Physical Society.
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